In this work, we derive a model to study and simulate the dynamics of power grids that, after a few approximations, turns out to be the second-order Kuramoto model. We then use this model to perform some numerical simulations that relate to the vulnerability and stability of energy transmission networks. In relation to the stability, assuming the grid is fully functional, and therefore, is in the synchronous state, we analyze how the grid responds to large perturbations, and also, how this response can be influenced by the location of the node being perturbed. We also show how a simple change in the topology or in the transmission capacity of a line can affect the synchronization of the grid. Regarding the vulnerability, some indexes to identify dynamically vulnerable nodes and edges are presented.

在这项工作中，我们推导出一个模型来研究和模拟电网的动力学，经过几次近似后，结果是二阶 Kuramoto 模型。然后我们使用这个模型来执行一些与能源传输网络的脆弱性和稳定性相关的数值模拟。关于稳定性，假设电网功能齐全，因此处于同步状态，我们分析电网如何响应大扰动，以及这种响应如何受到被扰动节点的位置的影响。我们还展示了拓扑或线路传输容量的简单变化如何影响电网的同步。针对该漏洞，提出了一些动态识别易受攻击的节点和边的指标。